Temperature controller for semiconductor wafer and temperature control method for semiconductor wafer

ABSTRACT

A temperature controller that performs a temperature control on a plurality of temperature adjusters including a reference temperature adjuster to adjust a temperature of a semiconductor wafer includes a setpoint setting section that: sets a temperature detected by a master temperature detector as a control setpoint for a reference one of the temperature adjusters of a master loop, until a temporary setpoint below an actual control setpoint preset as a desired temperature of the semiconductor wafer is reached; and sets the actual control setpoint as the control setpoint for the master loop after the temporary setpoint is reached.

The entire disclosure of Japanese Patent Application No. 2014-012293filed Jan. 27, 2014 is expressly incorporated herein by referenceherein.

TECHNICAL FIELD

The present invention relates to a temperature controller for asemiconductor wafer and a temperature control method for a semiconductorwafer that are configured to perform a temperature control on aplurality of temperature adjusters to adjust the temperature of thesemiconductor wafer.

BACKGROUND ART

A process for treating a semiconductor wafer such as a silicon waferincludes controlling the in-plane temperature distribution of thesilicon wafer as desired while controlling the temperature of thesilicon wafer to a temperature setpoint.

For instance, according to a known method, heaters are each incorporatedin an independent control loop so that the semiconductor wafer issimultaneously heated using a plurality of temperature adjusters.

Regarding the above temperature control for a semiconductor wafer, it isnecessary that control variables should have a constant deviation from areference control variable until the temperature reaches a setpoint andthat the temperature should be maintained at the setpoint irrespectiveof any disturbance. In connection with the above, a master-slave controlmethod and a gradient temperature control method are typically known(see, for instance, Patent Literature 1: JP-A-7-200076 and PatentLiterature 2: JP-A-2000-187514).

In the master-slave control method, one of a plurality of control loopsis controlled as a master, and a deviation between a control variable (asetpoint) of the master loop and a control variable of a slave loop(s)is calculated and controlled so that the slave loop(s) follows thebehavior of the master loop.

In the gradient temperature control method, an average of controlvariables for loops is defined as a representative variable, and adifference between the control variables for the loops is defined as agradient variable (another control variable), the representativevariable following a setpoint with the gradient variable being keptconstant. The control variables are transformed using a transformationmatrix. Further, a non-interfering matrix is used to reduce interferenceamong the loops, and a manipulated variable transformation matrix isused to return the control variables to the original dimension.

However, the techniques disclosed in Patent Literatures 1 and 2 have aproblem of lowering a control performance because when the temperatureadjusters (an actuator) undergo saturation in the process of respondingto the setpoint, further compensation is unavailable.

SUMMARY OF THE INVENTION

An object of the invention is to provide a temperature control systemfor a semiconductor wafer and a temperature control method for asemiconductor wafer that ensure the following ability and uniformity ofcontrol variables among loops and allow temperature adjusters to respondto a setpoint almost at the fastest possible speed.

In a first aspect of the invention,

a temperature controller for a semiconductor wafer, the temperaturecontroller being configured to perform a temperature control on aplurality of temperature adjusters including a reference temperatureadjuster to adjust a temperature of the semiconductor wafer, includes:

a master loop configured to control a temperature of the referencetemperature adjuster;

at least one slave loop configured to follow the master loop to controla temperature of rest of the temperature adjusters;

a master temperature detector configured to detect the temperature ofthe semiconductor wafer having been adjusted by the referencetemperature adjuster;

a slave temperature detector configured to detect the temperature of thesemiconductor wafer having been adjusted by the rest of the temperatureadjusters; and

a manipulated variable calculator configured to calculate, from thetemperature detected by the master temperature detector and thetemperature detected by the slave temperature detector, a manipulatedvariable for the reference temperature adjuster and a manipulatedvariable for the rest of the temperature adjusters, the manipulatedvariable calculator including:

-   -   a setpoint setting section configured to set, as a control        setpoint for the reference temperature adjuster, an actual        control setpoint preset as a desired temperature of the        semiconductor wafer or a value equal to the temperature detected        by the master temperature detector;    -   a master deviation calculator configured to calculate a        deviation between the control setpoint set by the setpoint        setting section and the temperature detected by the master        temperature detector;    -   a slave deviation calculator configured to calculate a deviation        between the temperature detected by the master temperature        detector and the temperature detected by the slave temperature        detector;    -   a master control calculator configured to receive the deviation        calculated by the master deviation calculator to calculate the        manipulated variable for the reference temperature adjuster;    -   a slave control calculator configured to receive the deviation        calculated by the slave deviation calculator to calculate the        manipulated variable for the rest of the temperature adjusters;    -   a manipulated variable converter configured to output the        manipulated variable calculated by the master control calculator        and the manipulated variable calculated by the slave control        calculator respectively to the reference temperature adjuster        and the rest of the temperature adjusters after converting the        manipulated variable calculated by the master control calculator        and the manipulated variable calculated by the slave control        calculator so that interference between the master loop and the        slave loop is reduced; and    -   a feedforward variable adding section configured to add a        predetermined feedforward variable corresponding to an output        from the manipulated variable converter, in which

the setpoint setting section: sets the temperature detected by themaster temperature detector as the control setpoint for the referencetemperature adjuster, until a temporary setpoint below the actualcontrol setpoint is reached; and sets the actual control setpoint as thecontrol setpoint for the reference temperature adjuster after thetemporary setpoint is reached.

In a second aspect of the invention, the temporary setpoint includes aplurality of temporary setpoints.

In a third aspect of the invention, it is determined whether or not thetemporary setpoint is reached on a basis of at least one of temperatureand time.

In a fourth aspect of the invention,

a temperature control method for a semiconductor wafer, the temperaturecontrol method being configured to perform a temperature control on aplurality of temperature adjusters including a reference temperatureadjuster to adjust a temperature of the semiconductor wafer, theplurality of temperature adjusters being controlled by a temperaturecontrol system, the temperature control system including:

a master loop configured to control a temperature of the referencetemperature adjuster;

at least one slave loop configured to control a temperature of rest ofthe temperature adjusters; and

a manipulated variable calculator configured to apply a manipulatedvariable to each of the reference temperature adjuster and the rest ofthe temperature adjusters,

the temperature control method being configured to be performed by themanipulated variable calculator, the temperature control methodincludes:

setting, as a control setpoint for the master loop, a temperaturedetection value of the semiconductor wafer having been subjected to atemperature adjustment by the temperature adjusters;

performing the temperature control of the temperature adjusters based ona preset feedforward variable;

determining whether or not a temporary setpoint below an actually presetcontrol setpoint to be finally achieved is reached;

switching the control setpoint for the master loop to the controlsetpoint to be finally achieved, when the temporary setpoint isdetermined to be reached; and

performing a feedback control in combination with a feedforward controlbased on a preset feedforward variable.

In the first aspect of the invention, the setpoint setting section: setsa temperature detected by the master temperature detector as a controlsetpoint for the reference temperature adjuster of the master loop,until a temporary setpoint below an actual control setpoint, which ispreset as a desired temperature of the semiconductor wafer, is reached;and sets the actual control setpoint as the control setpoint for thereference temperature adjuster after the temporary setpoint is reached.

Therefore, since the temperature detection value is set as the controlsetpoint to be achieved until the temporary setpoint is reached, afeedback control of the temperature detection value is cancelled andthus is not performed.

As a result, at the start of the temperature adjustment control, thetemperature adjustment can be performed based on the feedforwardvariable almost at the fastest possible speed of the temperatureadjuster of the master loop.

After the temporary setpoint is reached, a typical feedback control isperformed in combination with the feedforward control so that thecontrol setpoint is promptly reached.

In the second aspect of the invention, a plurality of temporarysetpoints are preset, thereby further minutely determining feedforwardvariables to achieve a highly accurate temperature control.

In the third aspect of the invention, it is determined whether or notthe temporary setpoint is reached on a basis of at least one oftemperature and time, thereby achieving a highly accurate temperatureadjustment control.

The fourth aspect of the invention can provide effects similar to thoseof the first aspect.

BRIEF DESCRIPTION OF DRAWING(S)

FIG. 1 is a block diagram showing a temperature adjustment apparatusaccording to a first exemplary embodiment of the invention.

FIG. 2A is a sectional view showing an arrangement of a heater and atemperature sensor according to the first exemplary embodiment.

FIG. 2B is a plan view showing an arrangement of the heater and thetemperature sensor according to the first exemplary embodiment.

FIG. 3 is a block diagram showing a structure of a controller thatcontrols the temperature adjustment apparatus according to the firstexemplary embodiment.

FIG. 4 is graphs for explaining the effects of the first exemplaryembodiment, showing a relationship between a control variable PV and amanipulated variable MV.

FIG. 5 is graphs for explaining the effects of the first exemplaryembodiment, showing a relationship between the control variable PV andthe manipulated variable MV.

FIG. 6 is a flow chart for explaining the effects of the first exemplaryembodiment.

FIG. 7 is graphs for explaining the effects of a second exemplaryembodiment of the invention, showing a relationship between the controlvariable PV and the manipulated variable MV.

FIG. 8A is a graph for explaining the result of a simulation accordingto the first exemplary embodiment, showing a variation of the controlvariable PV (in the case that a target without interference iscontrolled).

FIG. 8B is a graph for explaining the result of the simulation accordingto the first exemplary embodiment, showing a variation of themanipulated variable MV (in the case that the target withoutinterference is controlled).

FIG. 9A is a graph for explaining the result of a simulation by atypical method, showing a variation of the control variable PV (in thecase that the target without interference is controlled).

FIG. 9B is a graph for explaining the result of the simulation by thetypical method, showing a variation of the manipulated variable MV (inthe case that the target without interference is controlled).

FIG. 10A is a graph for explaining the result of a simulation by atypical gradient temperature control method, showing a variation of thecontrol variable PV (in the case that the target without interference iscontrolled).

FIG. 10B is a graph for explaining the result of the simulation by thetypical gradient temperature control method, showing a variation of themanipulated variable MV (in the case that the target withoutinterference is controlled).

FIG. 11 schematically illustrates a model designed to have interferenceamong temperature adjusters.

FIG. 12A is a graph for explaining the result of the simulationaccording to the first exemplary embodiment, showing a variation of thecontrol variable PV (in the case that the target with interference iscontrolled).

FIG. 12B is a graph for explaining the result of the simulationaccording to the first exemplary embodiment, showing a variation of themanipulated variable MV (in the case that the target with interferenceis controlled).

FIG. 13A is a graph for explaining the result of the simulation by thetypical method, showing a variation of the control variable PV (in thecase that the target with interference is controlled).

FIG. 13B is a graph for explaining the result of the simulation by thetypical method, showing a variation of the manipulated variable MV (inthe case that the target with interference is controlled).

FIG. 14A is a graph for explaining the result of the simulation by thetypical gradient temperature control method, showing a variation of thecontrol variable PV (in the case that the target with interference iscontrolled).

FIG. 14B is a graph for explaining the result of the simulation by thetypical gradient temperature control method, showing a variation of themanipulated variable MV (in the case that the target with interferenceis controlled).

DESCRIPTION OF EMBODIMENT(S)

Exemplary embodiment(s) of the invention will be described below withreference to the attached drawings.

[1] Structure of Temperature Adjustment Apparatus 1

FIG. 1 shows a temperature adjustment apparatus 1 according to a firstexemplary embodiment of the invention. The temperature adjustmentapparatus 1 controls the temperature of a silicon wafer W set on a stage2 to a temperature setpoint and controls the in-plane temperaturedistribution of the silicon wafer W. The temperature adjustmentapparatus 1 is used, for instance, in a dry process.

The temperature adjustment apparatus 1 includes the stage 2 and a heater3. It should be noted that the stage 2, which is heated by the heater 3in the first exemplary embodiment, may alternatively be heated by achiller or a thermoelectric element, and a cooling control may beperformed in the case of using the chiller or the thermoelectricelement.

The stage 2 is disposed in a vacuum chamber 4 and the silicon wafer W isset on the stage 2. The silicon wafer W is electrostatically held on thestage 2. It should be noted that helium gas may be delivered between thestage 2 and the silicon wafer W to enhance efficiency in heat transferbetween the stage 2 and the silicon wafer W.

In the dry process, the vacuum chamber 4 is vacuumized and maintained ina predetermined low-pressure state.

As shown in FIGS. 2A and 2B, the heater 3 includes a plurality ofheaters 3 disposed in the stage 2 to adjust the in-plane temperaturedistribution of the silicon wafer W on the stage 2.

FIG. 2A is a sectional view of the stage 2, showing that a plate 5 isdisposed on the heaters 3 on the stage 2. A temperature sensor 6 (atemperature detector) is disposed in the plate 5.

FIG. 2B is a plan view of the stage 2, showing that the stage 2 isdivided into three concentric zones 2A, 2B, 2C, in each of which theheaters 3 are disposed. The temperature sensor 6 in the plate 5 includestemperature sensors 6 disposed at positions corresponding to the heaters3.

The zones 2A, 2B and 2C of the stage 2 can be independently heated bysupplying electricity to the heaters 3. Accordingly, the heaters 3 arecontrolled by adjusting the supply of electricity thereto to adjust thein-plane temperature distribution of the silicon wafer W on the stage 2.The heaters 3 disposed in each of the zones 2A, 2B and 2C are controlledby a controller 24.

[2] Structure of Controller 24

The controller 24 controls the heaters 3, which include master heaters3M and slave heaters 3S, based on temperatures detected by thetemperature sensor 6 as described above, and has a functional structureas shown in a block diagram of FIG. 3.

The controller 24 includes: a master loop MR for controlling the heaters3M for heating the zone 2A shown in FIGS. 2A and 2B; a slave loop SR forcontrolling the heaters 3S for heating the zone 2B and the zone 2C; amaster temperature sensor 6M that detects the temperatures of theheaters 3M; a slave temperature sensor 6S that detects the temperaturesof the heaters 3S; and a manipulated variable calculator 30 thatcalculates a manipulated variable for each of the master loop MR and theslave loop SR. It should be noted that the slave loop SR includes twoloops for the zones 2B, 2C that similarly follow the master loop MR, andthus only one of the loops is shown in FIG. 3.

In a master-slave control system, a control variable for a slave sidefollows a control variable for a master side to control the temperaturedistribution. Accordingly, the maximum response speed of the controlsystem is usually limited by a loop with the slowest response speed, sothat the loop with the slowest response speed should be defined as themaster loop MR.

The manipulated variable calculator 30 applies manipulated variablesMVm, MVs based on a master control setpoint SVm and a slave controlsetpoint SVs to the heaters 3M, 3S, respectively.

The manipulated variable calculator 30 includes: a setpoint settingsection 31, a switch 32, a master deviation calculator 33M, a slavedeviation calculator 33S, a master control calculator 34M, a manipulatedvariable converter 35, a master feedforward variable adding section 36M,a slave feedforward variable adding section 36S, a master manipulatedvariable regulator 37M, a slave manipulated variable regulator 37S, anoffset setting section 38 and a setpoint filter 39.

The setpoint setting section 31 monitors a temperature detection valuePVm from the temperature sensor 6M of the master loop MR, and switchesthe switch 32 when the temperature detection value reaches a presettemporary setpoint X (described later). At the start of an operation,the switch 32 is initially set in a first position for setting thetemperature detection value PVm from the temperature sensor 6M as themaster control setpoint SVm. When determining that the temperaturedetection value PVm from the temperature sensor 6M reaches the temporarysetpoint X, the setpoint setting section 31 switches the switch 32 to asecond position for setting an actually preset control setpoint as themaster control setpoint SVm. It should be noted that the controlsetpoint SV may be SVf inputted through the setpoint filter 39.

The setpoint setting section 31 varies a feedforward variable FFm to beadded to the master feedforward variable adding section 36M and afeedforward variable FFs to be added to the slave feedforward variableadding section 36S, while monitoring the temperature detection valuePVm.

The master deviation calculator 33M calculates a deviation em betweenthe control setpoint SVm inputted through the switch 32 and thetemperature detection value PVm from the temperature sensor 6M, andoutputs it to the master control calculator 34M.

The slave deviation calculator 33S calculates a deviation es between theslave control setpoint SVs, which is the temperature detection value PVmfrom the master temperature sensor 6M, and the detection value PVs fromthe slave temperature sensor 6S, and outputs it to the slave controlcalculator 34S. When a constant temperature difference is to be providedbetween the master and the slave, a temperature difference δ is set inthe offset setting section 38.

The master control calculator 34M, an example of which is a PIDcontroller, outputs a calculation result Um to the manipulated variableconverter 35.

The slave control calculator 34S similarly outputs a calculation resultUs to the manipulated variable converter 35.

The manipulated variable converter 35 is configured to convert theinputted calculation result Um from the master control calculator 34Mand calculation result Us from the slave control calculator 34S intomanipulated variables so that mutual interference between the masterloop MR and the slave loop SR is reduced. The two inputs Um, Us areconverted into the two outputs Vm, Vs using a transformation matrix Hand the thus-obtained master manipulated variables Vm and slavemanipulated variable Vs are outputted. The transformation matrix H isobtained from, for instance, a steady-state gain matrix Gp=P(0) and amaster-slave manipulated variable transformation matrix Gm, given that atarget to be controlled is represented by a transfer function matrixP(s). The transformation matrix H for obtaining the manipulatedvariables is represented by the following formula (1), given that thetransfer function matrix P(s) has two rows and two columns.

$\begin{matrix}{\begin{matrix}{\begin{bmatrix}V_{m} \\V_{s}\end{bmatrix} = {H \cdot \begin{bmatrix}U_{m} \\U_{s}\end{bmatrix}}} \\{= {\begin{bmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{bmatrix}\begin{bmatrix}U_{m} \\U_{s}\end{bmatrix}}}\end{matrix}{H = \left( {{Gm} \cdot {Gp}} \right)^{- 1}}{{Gp} = {P(0)}}} & (1)\end{matrix}$

The master feedforward variable adding section 36M adds the feedforwardvariable FFm to the master output Vm from the manipulated variableconverter 35, whereas the slave feedforward variable adding section 36Sadds the feedforward variable FFs to the slave output Vs.

The master manipulated variable regulator 37M regulates the manipulatedvariable so that the output of the heaters 3M falls within a range fromthe minimum output to the maximum output thereof. When determining thatthe manipulated variable reaches a saturation level, the mastermanipulated variable regulator 37M outputs a corresponding determinationsignal awm to the master control calculator 34M. The output of themaster manipulated variable regulator 37M is outputted as themanipulated variable MVm to the heaters 3M.

Similarly, the slave manipulated variable regulator 37S regulates themanipulated variable so that the output of the heaters 3S falls within arange from the minimum output to the maximum output thereof. Whendetermining that the manipulated variable reaches a saturation level,the slave manipulated variable regulator 37S outputs a correspondingdetermination signal aws to the slave control calculator 34S. The outputof the slave manipulated variable regulator 37S is outputted as themanipulated variable MVs to the heaters 3S. The determination signalsawm, aws function as anti-windup activation signals in the mastercontrol calculator 34M and the slave control calculator 34S,respectively.

[3] Effects of First Exemplary Embodiment

FIG. 4 shows setpoint responses through a single-input single-outputsystem. FIG. 4(A) shows a temporal variation of the control variable PVand FIG. 4(B) shows a temporal variation of the manipulated variable MV.

In setpoint response through a control system in which the heaters 3Mcould be saturated, the control setpoint SV can be reached in theshortest time by: saturating the heaters 3M with a manipulated variableff₁, which enables the maximum output of the heaters 3M, so that thetemperature is increased at the maximum speed; switching the manipulatedvariable to zero before the control setpoint SV is reached (themanipulated variable may be set at a minus in the case of using athermoelectric element capable of heating and cooling); letting thecontrol setpoint SV be automatically reached (the control setpoint SVmay be reached with a braking force in the case of a minus manipulatedvariable); and finally immediately switching the manipulated variable toff₂ enabling the temperature to be settled at the control setpoint SV.

The above operation method is considerably difficult to perform under afeedback control such as a PID control in which a variable is calculatedbased on a deviation, and thus a feedforward control is suitablyemployed.

The first exemplary embodiment is based on the above idea. Specifically,as shown in FIG. 5, the setpoint setting section 31 performs a controlusing the switch 32 to: set the temperature detection value PVm from thetemperature sensor 6M as the control setpoint, when the manipulatedvariable PV is in a range A defined below the temporary setpoint X belowthe control setpoint SV; and set the actually preset control setpoint orSvf, which is inputted through the setpoint filter 39, as the controlsetpoint, when the manipulated in a range B over the temporary setpointX.

As a result, when the temperature detection value PVm is set as thecontrol setpoint SVm, the deviation between the control setpoint SVm andthe temperature detection value PVm calculated by the master deviationcalculator 33M is zero, so that the sum of the feedforward variable ff₁in the range A and a correction signal (e.g., h12×Us, in the formula(1)) outputted from the slave side through the transformation matrix His set as the manipulated variable for driving the heaters 3M.

In driving the heaters 3M of the master loop MR with the maximum output,a feedforward variable ff_(1s) for the heaters 3S of the slave loop SRcan be calculated using a steady-state gain matrix Gp in the aboveformula (1).

Specifically, a gain ratio g of an output in response to the input ofthe manipulated variable MV with the same magnitude can be obtained bythe following formula (2).

$\begin{matrix}\begin{matrix}{G_{p} = {P(0)}} \\{= \begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix}}\end{matrix} & \; \\{\begin{matrix}{g = \begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}} \\{= {\begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix} \cdot \begin{bmatrix}1 \\1\end{bmatrix}}} \\{= \begin{bmatrix}{k_{11} + k_{12}} \\{k_{21} + k_{22}}\end{bmatrix}}\end{matrix}\;{Let}\text{}\begin{matrix}{G_{p} = {P(0)}} \\{= \begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix}}\end{matrix}{Then}} & (2) \\\begin{matrix}{g = \begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}} \\{= {\begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix} \cdot \begin{bmatrix}1 \\1\end{bmatrix}}} \\{= \begin{bmatrix}{k_{11} + k_{12}} \\{k_{21} + k_{22}}\end{bmatrix}}\end{matrix} & (2)\end{matrix}$

Therefore, when g₂>g₁,ff _(1m)=100% (master side)ff _(1s)=100×(k ₁₁ +k ₁₂)/(k ₂₁ +k ₂₂)% (slave side)

On the other hand, when g₂<g₁,ff _(1m)=100×(k ₂₁ +k ₂₂)/(k ₁₁ +k ₁₂)% (master side)ff _(1s)=100% (slave side)The above values are set as initial values and adjusted by simulation,experiment with actual equipment, or the like.

A master feedforward variable ff_(2m) and a slave feedforward variableff_(2s) in the range B are calculated as follows.

When outputs in response to the input of the manipulated variable MV areequally the setpoint SV to be finally achieved, an input-outputrelationship in a steady state is represented by the following formula(3) using the steady-state gain matrix Gp.

$\begin{matrix}{\begin{bmatrix}{SV} \\{SV}\end{bmatrix} = {\begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix} \cdot \begin{bmatrix}{MV}_{m} \\{MV}_{s}\end{bmatrix}}} & (3)\end{matrix}$

Therefore, the master feedforward variable ff_(2m) and the slavefeedforward variable ff_(2s) are equal to the manipulated variable inthe steady state and thus can be calculated by the following formula(4).

$\begin{matrix}{\begin{bmatrix}{ff}_{2m} \\{ff}_{2m}\end{bmatrix} = {\begin{bmatrix}k_{11} & k_{12} \\k_{21} & k_{22}\end{bmatrix}^{- 1} \cdot \begin{bmatrix}{SV} \\{SV}\end{bmatrix}}} & (4)\end{matrix}$

A trial-and-error approach such as simulation or experiment with actualequipment is required to determine the temporary setpoint X. Inswitching the setpoint from X to SV in the range B, it is preferablethat the setpoint should be gradually changed through the setpointfilter 39 to the setpoint to be finally achieved because a drasticchange of the setpoint is accompanied by a drastic change of themanipulated variable, which may result in an unfavorable influence onthe control. For instance, a first order lag filter is used as thesetpoint filter 39, but it is not requisite. A trial-and-error approachis also required to determine a filter time constant. In the case ofusing a first order lag filter with a time constant of Tf seconds,SV_(f) is represented by the following formula (5).

$\begin{matrix}{{SV}_{f} = {\frac{1}{{T_{f}s} + 1}{SV}}} & (5)\end{matrix}$

It should be noted that the ranges are defined on a basis of temperaturein the first exemplary embodiment, but may be defined on a basis of acombination of temperature and time.

Next, a specific process of the first exemplary embodiment will bedescribed with reference to a flow chart shown in FIG. 6.

First, the setpoint setting section 31 sets the temperature detectionvalue PVm detected by the temperature sensor 6 as the setpoint SVm (stepS1), and starts driving of the heaters 3M of the master loop MR under afeedforward control mainly based on the feedforward variable ff_(1m)(step S2). Simultaneously, the setpoint setting section 31 startsdriving of the slave loop SR under a feedforward control based on thefeedforward variable ff_(1s) and a feedback control based on a slavedeviation es (step S3).

The setpoint setting section 31 monitors the temperature detection valuePVm detected by the temperature sensor 6 and determines whether or notthe temporary setpoint X is reached (step S4).

When the temporary setpoint X is determined to be reached, the setpointsetting section 31 sets the actually preset control setpoint SV or SVf,which is inputted through the setpoint filter 39, as the master controlsetpoint SVm using the switch 32 (step S5), and starts the feedbackcontrol of the master heaters 3M based on the feedforward control basedon the feedforward variable ff_(2m) and the feedback control based onthe master deviation em (step S6). The setpoint setting section 31starts driving of the slave heaters 3S based on the feedforward variableff_(2s) and the slave deviation es (step S7).

[4] Second Exemplary Embodiment

Next, a second exemplary embodiment of the invention will be described.It should be noted that, in the following description, parts and thelike identical to those described above are attached with the samereference signs and the explanation thereof is omitted.

In the first exemplary embodiment, when the temporary setpoint X isreached, the manipulated variable is immediately switched from thefeedforward variable ff₁ to the feedforward variable ff₂ as shown inFIG. 5.

In contrast, the second exemplary embodiment is different from the firstexemplary embodiment in that the manipulated variable is switched asshown in FIG. 7.

Specifically, in the second exemplary embodiment, the range A is furtherdivided into a plurality of ranges and feedforward variables areswitched in accordance with these ranges to achieve a further minutecontrol as shown in FIG. 7(B). The second exemplary embodiment isdifferent from the first exemplary embodiment in that the range A isdivided into a range A0 and a range A1 with reference to the temporarysetpoint Y, and the feedforward variables ff_(m10), ff_(s10) are addedin the range A0 whereas the feedforward variables ff_(m11), ff_(s11) areadded in the range A1.

The second exemplary embodiment can provide effects similar to those ofthe first exemplary embodiment.

[5] Demonstration of Effects of Invention

In order to demonstrate the effects of the invention, the methodaccording to the first exemplary embodiment, a typical master-slavecontrol method and the gradient temperature control method disclosed inthe publication of Japanese Patent No. 3278807 were each applied to theheaters 3M, 3S (a three-input three-output system), and the resultingsetpoint responses were compared.

[5-1] Target without Interference to be Controlled

A transfer function of the heaters 3 (a target to be controlled) wasrepresented by the following formula (6).

$\begin{matrix}{\begin{bmatrix}y_{1} \\y_{2} \\y_{3}\end{bmatrix} = {\quad{\begin{bmatrix}\frac{1.2\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{70s} + 1} \right)\left( {{10s} + 1} \right)} & 0 & 0 \\0 & \frac{1.6\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{60s} + 1} \right)\left( {{10s} + 1} \right)} & 0 \\0 & 0 & \frac{2.0\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{50s} + 1} \right)\left( {{10s} + 1} \right)}\end{bmatrix}\begin{bmatrix}u_{1} \\u_{2} \\u_{3}\end{bmatrix}}}} & (6)\end{matrix}$

The steady-state gain matrix Gp of this target was represented by thefollowing formula (7).

$\begin{matrix}{G_{p} = \begin{bmatrix}1.2 & 0 & 0 \\0 & 1.6 & 0 \\0 & 0 & 2\end{bmatrix}} & (7)\end{matrix}$

The gain ratio g was calculated by the above formula. When an arbitraryvalue such as 1 was assigned, the gain ratio g was represented by thefollowing formula (8).

$\begin{matrix}\begin{matrix}{g = \begin{bmatrix}g_{1} \\g_{2} \\g_{3}\end{bmatrix}} \\{= {G_{p}^{- 1}\begin{bmatrix}1 \\1 \\1\end{bmatrix}}} \\{= {\begin{bmatrix}1.2 & 0 & 0 \\0 & 1.6 & 0 \\0 & 0 & 2\end{bmatrix}^{- 1}\begin{bmatrix}1 \\1 \\1\end{bmatrix}}} \\{= \begin{bmatrix}0.833 \\0.625 \\0.5\end{bmatrix}}\end{matrix} & (8)\end{matrix}$

Based on the above ratio, the feedforward variable in the range A wasdetermined as ff₁=[100 75 60](%) based on ff_(1m), ff_(1s) calculated bythe formula (2).

The feedforward variable ff₂ in the range B was represented by thefollowing formula (9) when the setpoint was, for instance, 30.

$\begin{matrix}\begin{matrix}{{ff}_{2} = {G_{p}^{- 1}\begin{bmatrix}30 \\30 \\30\end{bmatrix}}} \\{= {\begin{bmatrix}1.2 & 0 & 0 \\0 & 1.6 & 0 \\0 & 0 & 2\end{bmatrix}^{- 1}\begin{bmatrix}30 \\30 \\30\end{bmatrix}}} \\{= {\begin{bmatrix}25 \\18.8 \\15\end{bmatrix}(\%)}}\end{matrix} & (9)\end{matrix}$

A PID controller was used as the controller and the manipulated variable(%) was set at a value calculated by the following formula (10). Itshould be noted that Pb represents a proportional range, Ti representsan integral time, and Td represents a derivative time.

$\begin{matrix}{{MV}_{n} = {{\frac{100}{{Pb}_{n}}\left( {1 + \frac{1}{{Ti}_{n}s} + \frac{{Td}_{n\;}s}{{{Td}_{n}{s/10}} + 1}} \right)e_{n}\mspace{31mu} n} = {1\mspace{14mu}\ldots\mspace{14mu} 3}}} & (10)\end{matrix}$

After the above preparation was done, a simulation by the methodaccording to the first exemplary embodiment, a simulation by the typicalmaster-slave method and a simulation by the gradient temperature controlmethod disclosed in Japanese Patent No. 3278807 were performed. Theresults of the above simulations are respectively shown in FIGS. 8A and8B, FIGS. 9A and 9B, and FIGS. 10A and 10B.

It should be noted that PID constants used in any of the abovesimulations were as follows.

MV1, PV1: Pb=100, Ti=35, Td=20

MV2, PV2: Pb=40, Ti=35, Td=20

MV3, PV3: Pb=40, Ti=35, Td=20

As a result of the above comparison, it is proved that the methodaccording to the first exemplary embodiment achieves early rise time andexcellent uniformity.

[5-2] Target with Interference to be Controlled

Next, regarding a target with interference to be controlled, the methodaccording to claim 1, the typical master-slave method and the gradienttemperature control method disclosed in Japanese Patent No. 3278807 werecompared.

Specifically, it was assumed that an aluminum plate as shown in FIG. 11was heated using heating elements (resistance) at three spots (Z1 toZ3). From the result of an experiment on dynamic characteristics, thetransfer function of the target to be controlled was represented by thefollowing formula (11).

$\begin{matrix}{\begin{bmatrix}y_{1} \\y_{2} \\y_{3}\end{bmatrix} = {\begin{bmatrix}\frac{42.7\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{297s} + 1} \right)} & \frac{22.2\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{432s} + 1} \right)} & \frac{19.6\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{484s} + 1} \right)} \\\frac{22.8\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{434s} + 1} \right)} & \frac{36.9\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{305s} + 1} \right)} & \frac{32.5\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{383s} + 1} \right)} \\\frac{16.0\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{476s} + 1} \right)} & \frac{31.7\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{352s} + 1} \right)} & \frac{46.0\mspace{14mu}{\exp\left( {{- 2}s} \right)}}{\left( {{290s} + 1} \right)}\end{bmatrix}\begin{bmatrix}u_{1} \\u_{2} \\u_{3}\end{bmatrix}}} & (11)\end{matrix}$

The steady-state gain matrix Gp of the heating elements (the target) wasrepresented by the following formula (12).

$\begin{matrix}{G_{p} = \begin{bmatrix}42.7 & 22.2 & 19.6 \\22.8 & 36.9 & 32.5 \\16.0 & 31.7 & 46.0\end{bmatrix}} & (12)\end{matrix}$

The gain ratio g was calculated by the above formula. When an arbitraryvalue such as 1 was assigned, the gain ratio g was represented by thefollowing formula (13).

$\begin{matrix}\begin{matrix}{g = \begin{bmatrix}g_{1} \\g_{2} \\g_{3}\end{bmatrix}} \\{= {\begin{bmatrix}42.7 & 22.2 & 19.6 \\22.8 & 36.9 & 32.5 \\16.0 & 31.7 & 46.0\end{bmatrix}\begin{bmatrix}1 \\1 \\1\end{bmatrix}}} \\{= \begin{bmatrix}84.5 \\92.2 \\93.7\end{bmatrix}}\end{matrix} & (13)\end{matrix}$

Based on the above ratio, the feedforward variable in the range A wasdetermined as ff₁=[100 92 90](%).

The feedforward variable ff₂(%) in the range B was represented by thefollowing formula (14) when the setpoint was, for instance, 40.

$\begin{matrix}\begin{matrix}{{ff}_{2} = {G_{p}^{- 1}\begin{bmatrix}40 \\40 \\40\end{bmatrix}}} \\{= {\begin{bmatrix}42.7 & 22.2 & 19.6 \\22.8 & 36.9 & 32.5 \\16.0 & 31.7 & 46.0\end{bmatrix}^{- 1}\begin{bmatrix}40 \\40 \\40\end{bmatrix}}} \\{= \left. \begin{bmatrix}0.549 \\0.374 \\0.421\end{bmatrix}\Rightarrow{\begin{bmatrix}54.9 \\37.4 \\42.1\end{bmatrix}(\%)} \right.}\end{matrix} & (14)\end{matrix}$

The feedforward variable ff₁ was switched to the feedforward variableff₂ at y1=37 degrees C. The temperature setpoint was changed from 37degrees C. to 40 degrees C. through a first order lag filter with a timeconstant of 20 seconds.

A PID controller was used as the controller and the manipulated variable(%) was set at a value calculated by the following formula (10).

PID constants used in any of the above simulations were as follows.

MV1, PV1: Pb=3.3, Ti=100, Td=0

MV2, PV2: Pb=3.3, Ti=100, Td=0

MV3, PV3: Pb=3.3, Ti=100, Td=0

A non-interfering matrix as represented by the following formula (15)was obtained by a commonly known method.

$\begin{matrix}{{Gp} = \begin{bmatrix}0.9582 & 0.3426 & 0.2699 \\0.3502 & 0.8064 & 0.5656 \\0.2241 & 0.6003 & 1.0572\end{bmatrix}} & (15)\end{matrix}$

A manipulated variable transformation matrix for master-slave wasrepresented by the following formula (16).

$\begin{matrix}{{Gm} = \begin{bmatrix}1 & 0 & 0 \\{- 1} & 1 & 0 \\{- 1} & 0 & 1\end{bmatrix}} & (16)\end{matrix}$

A manipulated variable transformation matrix for the gradienttemperature control method is represented by the following formula (17).

$\begin{matrix}{{{Gm}\; 2} = \begin{bmatrix}{1/3} & {1/3} & {1/3} \\{- 1} & 1 & 0 \\0 & {- 1} & 1\end{bmatrix}} & (17)\end{matrix}$

A transformation matrix H1 obtained by combining the non-interferingmatrix represented by the formula (15) and the manipulated variabletransformation matrix was represented by the following formula (18) inthe case of master-slave.

$\begin{matrix}\begin{matrix}{{H\; 1} = \left( {{Gm} \cdot {Gp}} \right)^{- 1}} \\{= \begin{bmatrix}0.6944 & {- 0.4809} & {- 0.0575} \\0.6287 & 2.2892 & {- 1.0754} \\0.4417 & {- 1.1979} & 1.5687\end{bmatrix}}\end{matrix} & (18)\end{matrix}$

A transformation matrix H2 obtained by combining the non-interferingmatrix and the manipulated variable transformation matrix for thegradient temperature control method was represented by the followingformula (19).

$\begin{matrix}\begin{matrix}{{H\; 2} = \left( {{Gm}\;{2 \cdot {Gp}}} \right)^{- 1}} \\{= \begin{bmatrix}0.6944 & {- 1.0013} & {- 0.2890} \\0.6287 & 0.7947 & {- 1.2850} \\0.4417 & 0.0763 & 1.4214\end{bmatrix}}\end{matrix} & \left( 19 \right.\end{matrix}$

After the above preparation was done, a simulation by the methodaccording to the first exemplary embodiment, a simulation by the typicalmaster-slave method and a simulation by the gradient temperature controlmethod disclosed in Japanese Patent No. 3278807 were performed. Theresults of the above simulations are respectively shown in FIGS. 12A and12B, FIGS. 13A and 13B, and FIGS. 14A and 14B.

As a result, it is proved that the method according to the firstexemplary embodiment achieves early rise time and excellent uniformityirrespective of whether or not the target to be controlled suffersinterference.

What is claimed is:
 1. A temperature controller for a semiconductorwafer, the temperature controller performing a temperature control on aplurality of temperature adjusters including a reference temperatureadjuster to adjust a temperature of the semiconductor wafer, thetemperature controller comprising: a master loop, controlling atemperature of the reference temperature adjuster; at least one slaveloop, following the master loop to control a temperature of rest of thetemperature adjusters; a master temperature detector, detecting thetemperature of the semiconductor wafer having been adjusted by thereference temperature adjuster; a slave temperature detector, detectingthe temperature of the semiconductor wafer having been adjusted by therest of the temperature adjusters; and a manipulated variablecalculator, calculating, from the temperature detected by the mastertemperature detector and the temperature detected by the slavetemperature detector, a manipulated variable for the referencetemperature adjuster and a manipulated variable for the rest of thetemperature adjusters, the manipulated variable calculator comprising: asetpoint setting section, setting as a control setpoint for thereference temperature adjuster an actual control setpoint preset as adesired temperature of the semiconductor wafer or a value equal to thetemperature detected by the master temperature detector; a masterdeviation calculator, calculating a deviation between the controlsetpoint set by the setpoint setting section and the temperaturedetected by the master temperature detector; a slave deviationcalculator, calculating a deviation between the temperature detected bythe master temperature detector and the temperature detected by theslave temperature detector; a master control calculator, receiving thedeviation calculated by the master deviation calculator to calculate themanipulated variable for the reference temperature adjuster; a slavecontrol calculator, receiving the deviation calculated by the slavedeviation calculator to calculate the manipulated variable for the restof the temperature adjusters; a manipulated variable converter,outputting the manipulated variable calculated by the master controlcalculator and the manipulated variable calculated by the slave controlcalculator respectively to the reference temperature adjuster and therest of the temperature adjusters after converting the manipulatedvariable calculated by the master control calculator and the manipulatedvariable calculated by the slave control calculator so that interferencebetween the master loop and the slave loop is reduced; and a feedforwardvariable adding section, adding a predetermined feedforward variablecorresponding to an output from the manipulated variable converter,wherein the setpoint setting section: sets the temperature detected bythe master temperature detector as the control setpoint for thereference temperature adjuster, until a temporary setpoint below theactual control setpoint is reached; and sets the actual control setpointas the control setpoint for the reference temperature adjuster after thetemporary setpoint is reached.
 2. The temperature controller for thesemiconductor wafer according to claim 1, wherein the temporary setpointcomprises a plurality of temporary setpoints.
 3. The temperaturecontroller for the semiconductor wafer according to claim 1, wherein itis determined whether or not the temporary setpoint is reached on abasis of at least one of temperature and time.
 4. A temperature controlmethod for a semiconductor wafer, the temperature control methodperforming a temperature control on a plurality of temperature adjustersincluding a reference temperature adjuster to adjust a temperature ofthe semiconductor wafer, the plurality of temperature adjusters beingcontrolled by a temperature control system, the temperature controlsystem comprising: a master loop, controlling a temperature of thereference temperature adjuster; at least one slave loop, controlling atemperature of rest of the temperature adjusters; and a manipulatedvariable calculator, applying a manipulated variable to each of thereference temperature adjuster and the rest of the temperatureadjusters, the manipulated variable calculator comprising: a setpointsetting section, setting as a control setpoint for the referencetemperature adjuster an actual control setpoint preset as a desiredtemperature of the semiconductor wafer or a value equal to thetemperature detected by a master temperature detector that detects thetemperature of the semiconductor wafer having been adjusted by thereference temperature adjuster; a master deviation calculator,calculating a deviation between the control setpoint set by the setpointsetting section and the temperature detected by the master temperaturedetector, a slave deviation calculator, calculating a deviation betweenthe temperature detected by the master temperature detector and thetemperature detected by a slave temperature detector that detects thetemperature of the semiconductor wafer having been adjusted by the restthe of temperature adjusters, a master control calculator, receiving thedeviation calculated by the master deviation calculator to calculate themanipulated variable for the reference temperature adjuster, a slavecontrol calculator, receiving the deviation calculated by the slavedeviation calculator to calculate the manipulated variable for the restof the temperature adjusters, and a manipulated variable converter,outputting the manipulated variable calculated by the master controlcalculator and the manipulated variable calculated by the slave controlcalculator respectively to the reference temperature adjuster and therest of the temperature adjusters after converting the manipulatedvariable calculated by the master control calculator and the manipulatedvariable calculated by the slave control calculator so that interferencebetween the master loop and the slave loop is reduced; the temperaturecontrol method being performed by the manipulated variable calculator,the temperature control method comprising: setting, as a controlsetpoint for the master loop, a temperature detection value of thesemiconductor wafer having been subjected to a temperature adjustment bythe temperature adjusters; performing the temperature control of thetemperature adjusters based on a preset feedforward variable;determining whether or not a temporary setpoint below an actually presetcontrol setpoint to be finally achieved is reached; switching thecontrol setpoint for the master loop to the control setpoint to befinally achieved, when the temporary setpoint is determined to bereached; and performing a feedback control in combination with afeedforward control based on a preset feedforward variable.